A good stage actor can immerse you in his imaginary world. An outstanding one makes you feel you're the only other person in it. That higher-level mastery is achieved by Laurence Fishburne in "Thurgood," the warmly satisfying one-man show based on the life of the first African American to sit on the U.S. Supreme Court.

Fishburne portrayed the wily, irresistible Thurgood Marshall two years ago on Broadway and now, reprising the role for a three-week engagement in the Kennedy Center's Eisenhower Theater, he forges an even deeper mind-meld with one of the crucial figures of 20th-century American history. George Stevens Jr.'s bio-play, solidly staged by Leonard Foglia, persuasively confirms for us Marshall's pivotal contribution to the civil rights movement, as the victorious NAACP lawyer in the 1950s landmark desegregation case Brown v. Board of Education.

And in his embodiment of the proud, ambitious, restless Marshall, who took robustly to heart the idea that the law can be a powerful tool for social change, Fishburne cements a bond of astonishing intimacy with his audience. By the time he arrives at the end of the story, as an aged insider in one of the nation's most revered institutions, the actor will have completed the task of confiding the details of Marshall's life in a most entertainingly digestible way.

Yes, a dimension of hero worship is evident in Stevens's conventional script: What you get in "Thurgood" is a charm-infused recitation of the justice's accomplishments. (That litany includes Marshall's boasts of writing 98 majority opinions as a lower-court judge, none of which he says were overturned, and of writing opinions in 322 Supreme Court cases.)

Still, the play allows just enough of a glimpse of the failings of a living, breathing human being -- he mentions fondnesses for drink and women -- to stave off the lapse into hagiography. Make no mistake, though: This isn't tell-all dumpster diving for the TMZ generation. It's the survey of the extraordinary exertions of a gifted believer in the system -- a celebration, for a change, of the value of public service. In that regard, it's a play you might want to bring the kids to. And given the punishing obstacles to which Marshall was subjected, you really don't begrudge him or the play a bit of self-congratulation.

The premise of the brisk, 95-minute production is a nostalgic address by Marshall late in his life (he died in 1993) at his alma mater, Howard University School of Law. Thanks to Brian Nason's impressive lighting and the evocative projections by Elaine J. McCarthy, the set is transformed seamlessly for scenes in courtrooms and the more threatening locations to which Marshall's legal work took him. Allen Moyer's austere set is dominated by a giant, stylized rendering in white of an American flag, inspired by Jasper Johns's signature flags, and that becomes the screen for McCarthy's images.

Only a fraction of the evening is devoted to Marshall's quarter century on the high court. The real matters of "Thurgood" are the events and circumstances that cast him as a central player in Brown v. Board of Education. Some of the play's most absorbing moments revolve around Marshall's account of the case, particularly the arguments pro and con before the justices. Fishburne, a fine mimic, portrays Marshall as well as the courtly opposing counsel John W. Davis, and in the process brings to the fore the proceedings' resonant drama.

"Thurgood," in fact, accords Fishburne other delightful opportunities for thumbnail impersonations of figures as varied as Gen. Douglas MacArthur -- with whom Marshall locked horns over charges brought against a black soldier in Korea -- and President Lyndon B. Johnson, who nominated him to the seat he so coveted on the Supreme Court.

The actor also effectively channels Marshall's sly tongue. Recalling, for example, Martin Luther King Jr.'s embrace of Henry David Thoreau's famous essay on resisting authority, Fishburne's Marshall tells us how he'd try to bring King back to earth. "I would remind Martin that Thoreau wrote 'Civil Disobedience' in jail," he says.

It's Fishburne's enveloping bonhomie, his graceful engagement with the character, that elevate "Thurgood" to something more than standard-issue, fact-based drama. The portrayal's so alive you could claim with some justification that the great man spoke to you.

Thurgood, by George Stevens Jr. Directed by Leonard Foglia. Costumes, Jane Greenwood; sound, Ryan Rumery. About 95 minutes. Through June 20 at John F. Kennedy Center for the Performing Arts. Visit http://www.kennedy-center.org or call 202-467-4600.